The Language of Geometry

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point

a location that has no length, no width, and no thickness

line

an infinite set of points that extends in two directions but has length, but no width or thickness

plane

an infinite set of points which creates a flat surface that extends without ending (no edges) and it has length and width, but no thickness

space

the set of all points and needs 4 points to define space

collinear points

points on the same line

noncollinear points

points that do not lie on the same line (must describe at least 3 points)

coplanar points

points that exist in the same plane

noncoplanar points

points that do not exist in the same plane

intersection

the set of points that two geometric figures have in common

segment

consists of two points on a line and all points in between them

ray

a part of a line consisting of one endpoint all points on one side of the endpoint

opposite rays

two rays that share the same endpoint and together form a line *Point in opposite directions*

congruent

two objects that have the same size and shape

midpoint of a segment

point that divides a segment into own congruent segments

segment bisector

a line, segment, ray, or plane that divides a line segment into two congruent segments

angle

figure formed by two rays that have the same endpoint

right angle

angle whose measure is 90 degrees

acute angle

an angle whose measure is between 0 and 90 degrees

obtuse angle

an angle whose measure is between 90 and 180 degrees

straight angle

an angle whose measure is 180 degrees

congruent angles

angles that have equal measures

adjacent angles

two angles in a plane that have a common vertex and a common side but no common interior points

angle bisector

a ray that divides an angle into two congruent adjacent angles

postulates

statement that is accepted without proof

true or false: any three points are coplanar

true

true or false: any two points are collinear

true

true or false: collinear points are coplanar

true

true or false: coplanar points are always collinear

false

true or false: planes can intersect in a segment

false

true or false: two lines can intersect at two different points

false

true or false: a plane and a line can intersect at exactly two points

false

true or false: planes have no thickness

true

true or false: two vertical planes can intersect

true

true or false: two horizontal planes can intersect

false

two intersecting planes __ intersect in exactly one point

never

a line __ contains exactly one point

never

two points __ lie in exactly one line

always

if AB=BC, then B is __ the midpoint of segment AC

sometimes

if two points are in a plane, then the line that contains those points __ in that plane

always

two intersecting lines __ lie in exactly one plane

always

three points __ lie in exactly one line

sometimes

three points __ lie in exactly one plane

sometimes

three collinear points __ lie in exactly one plane

never

two planes __ intersect

sometimes

two lines __ intersect in exactly one point

sometimes

a line and a point not on a line __ lie in more than one plane

never

when A and B are in a plane, line AB is __ in that plane

always

coplanar points are __ collinear

never

planes __ have edges

never

there is __ a line through any three points

sometimes

two planes __ intersect in a line

never

two planes __ intersect in a point

sometimes

three points are __ coplanar

always

if two planes intersect, then their intersection is __ a segment

never

a line and a point not on a line are __ coplanar

sometimes